Scanning microscopy, including especially confocal scanning microscopy, is typified by an aperture which masks the incident light used to illuminate the specimen as well as the light returning from the specimen representative of the desired image. For purposes of clarity, the terms mask or masking will be used hereinafter and will be understood as referring to aperture effects in both the incident and return light paths. As is well known in the art of microscopy, enhanced contrast and resolution of an image may be obtained through scanning both the incident and reflected light. One of the inventors herein is also a co-inventor of the above-referenced patent applications which disclose and claim a new design for a confocal scanning microscope wherein a single aperture is used to scan both the incident and reflected light.
In the prior art, many different kinds of apertures have been proposed and used to achieve this scanning function in a confocal microscope. A widely used device is called a Nipkow disc which is typified by a series of small holes arranged in an Archimedes' spiral, with multiple spirals typically being contained in a single disc. Additionally, as most confocal scanning microscopes presently being used are of the tandem variety with a different light path for incident and reflected light, the Nipkow disc must contain matched pairs of spirals. As can be appreciated, it is difficult and, hence, expensive to accurately align and machine the large number of small holes generally contained in each Nipkow disc. For example, it is not uncommon for a Nipkow disc to contain 10,000 holes. As a result Nipkow discs can be quite expensive to manufacture and yet provide less than optimum performance due to potential misalignment of the holes at current manufacturing tolerances. Therefore, there exists in the art a need for a better aperture for use with a scanning microscope.
In considering the problem of an aperture for a scanning microscope, there are several conditions which must be met. One of these is that it is desirable to mask each portion of the specimen for the same fraction of scanning time in order to achieve a uniform masking across the entire specimen. If a specimen is subjected to uneven masking, then less information can be obtained from the image due to variations in brightness because contrast between light and dark areas of the specimen are important in analyzing the visual information derived from the specimen. A second condition is that each portion of the specimen be scanned through an opening which is equivalent in size to that used for scanning other portions of the specimen. It is a phenomenon of scanning microscopy that, generally speaking, the smaller the aperture, the more improved the image quality, providing greater detail (for example a narrower optical section or greater resolution) that is discernible to the viewer. A variation in the section thickness or resolution of the image data resulting from a variation in the size of the aperture used to scan various portions of the specimen renders an image of uneven quality which is less than desirable. Therefore, these two criteria, i.e. uniformity in the relative duration of mask time as well as uniformity in the size of the masked area, at every region of the specimen, are most important in considering an aperture for use in scanning microscopy.
For example, with a rotating pie-slice disc aperture whose center of rotation is at the apex of the wedge, the relative duration of masking at a point on the specimen is equal to that fractional portion of a circumference on the disc overlying the point which comprises the pie-slice. The resolving power for any aperture above any point on the specimen is proportional to the area being masked at any one instant. For the pie-slice disc aperture, this is related to the minimum distance between the pie-slice edges at the point of intersection of one such edge with the point of interest on the specimen. For a slit aperture, the distance between the inner and outer edges of the slit along a circumference of a circle whose center is at the origin of rotation, i.e. the "circumferential aperture distance", when divided by the total circumference, determines the relative duration of masking. The resolving power of the slit aperture is related to the minimum distance between the inner and outer edges at every such point, i.e. the "minimum slit width".
Applying these criteria to a Nipkow disc, it can be appreciated that uniform masking is quite difficult to achieve because of the inherent difficulties in precisely aligning all of the holes to eliminate scan lines which would otherwise result from areas of over or under scanning of the image. In other words, the path that the holes mask across the specimen could either overlap or underlap thereby resulting in scan lines and areas of uneven masking. Still another example of a partial solution to the problem of achieving an optimal aperture is the rotating disc with one or more parallel radial slits of equal width. While this aperture does not produce scan lines, the relative duration of masking becomes progressively less in areas of the specimen scanned by progressively more radially distant areas of the disc, thereby resulting in uneven masking. This is because the percentage of time and area that is masked is proportional to the percentage of the circumference comprising the slit at a given radial distance of the disc. Still another possible aperture, which would eliminate uneven masking, is a pie-slice shaped slit or slits having a width which is proportional to the radius. With this pie-slice shaped aperture, the duration of masking is uniform throughout the specimen. However, the resolution of the image will vary as a function of the radial distance as the size or width of the "aperture" varies radially. In other words, the pie-slice shaped opening is narrower near the center of the disc than it is at the outer edges of the disc, such that greater "masking" takes place for parts of the specimen closer to the center of the disc. Similarly, the progressively more centrifugal parts of the specimen will be masked with progressively wider swaths of light because the slit has a greater minimum slit width and experience lesser "masking". Therefore, the pie-slice shaped aperture is not a satisfactory solution to the problem as it leads to uneven image resolution.
To solve these and other problems in the prior art, the inventors herein have succeeded in designing and developing an aperture for use in scanning microscopy which provides both uniform masking and uniform resolution as the aperture has an opening with a constant minimum width and a constant proportional circumferential aperture distance. This new aperture comprises a continuous slit which is generally formed in the shape of an Archimedes' spiral. More exactly, a first edge of the slit is indeed an Archimedes' spiral emanating from the origin or center of rotation of the disc while the second or outer edge of the slit may be more exactly defined in either one of two ways which form the two embodiments of the present invention. The inner edge of both embodiments has the formula of a typical Archimedes' spiral of: ##EQU1##
This and other formulae herein are written in polar coordinates where r is the radius from the origin and .theta. is the angle in radians around the origin.
In the first embodiment, the outer edge of the slit is defined by the formula: ##EQU2## where a=the distance along a radius centered at the origin between the two edges (typically in the range of 10-30 microns) and .PHI.=the angle subtended by the arc delineated by the intersection of any circular circumference (centered at the origin) with the two edges. In the second embodiment, the outer edge of the slit may be simply defined as that locus of points offset from the inner edge in a manner such that the distance "a" to the outer spiral is taken along a line perpendicular to the local tangent at every point on the inner spiral, each such perpendicular line being also perpendicular to the local tangent where it intersects the outer spiral. In this sense the width of the slit is constant throughout and the formula for the outer edge of the slit is: ##EQU3##
With edges defined by formulae of this type, it can be shown that within several full revolutions of the spirals, the optimal conditions are achieved for both minimum slit width and constant proportional circumferential aperture distance. The difference between the two embodiments is that for the first, the circumferential aperture distance is exact and proportionately constant throughout whereas the minimum slit width is slightly low at the center but rapidly approaches the optimum width within a few rotations of the spiral; and for the second embodiment the minimum slit width is exact and constant throughout whereas the proportional circumferential aperture distance is larger than desired at the very center but approaches ideal similarly rapidly in a few revolutions of the spiral. In the first embodiment for example, if a is equal to 10 microns and .PHI. is equal to ##EQU4## radians, then within 4.pi. radians (two revolutions) the slit width is approximately 9.97 microns, only 0.03 microns from its limit value of 10 microns. Thus, within several revolutions, the slit has a minimum width which becomes negligibly different as a function of both radial and angular location, reaching a limit value of a. Similarly for the second embodiment, the proportional circumferential aperture distance is within 0.3% of its desired limit by the second revolution.
One difficulty with this approach, however, is that the rotating disc must be centered on the true center of the spirals. For example, an eccentricity of only 0.4 microns would produce a circumferential slit width error of .+-.2.5% using a single spiral with a =10 microns and ##EQU5## Even if the disc were centered precisely, the tolerances of bearings ("play") might be plus or minus several microns. Furthermore, centralization of the spiral on the glass plate also will have some error, conceivably 10-80 microns. Thus, the single spiral design would be difficult at current manufacturing tolerances to implement successfully.
Calculations show, however, that the sensitivity to eccentricity can be reduced substantially by increasing the pitch of the spiral (e.g. from 100 microns/revolution to 2000 microns by decreasing .PHI. from ##EQU6## With a 20 fold higher pitch a circumferential slit width error of .+-.2.5% now occurs when the spiral is eccentric by about 8 microns. With a 60 fold increase in pitch, a 23 micron eccentricity would produce the same circumferential slit width error. In order to restore the density of slits to the desired level while at the same time increasing the pitch, additional spirals of the same form would be added. These spirals would be phased appropriately in .theta.. For example, 10 spiral apertures of pitch 1000 microns and phased every ##EQU7## radians would restore the 100 micron spacing of aperture turns.
Calculations show that eccentricity of the spiral pattern manifests as phasic errors in circumferential slit width. Because of this, the addition of multiple spirals adds a second advantage: it reduces the sensitivity of eccentricity by allowing each spiral to help offset the errors of other spirals that are originating at different phases. For example, a two spiral pattern each having a pitch of 200 microns and 180.degree. apart with respect to rotation about the geometric center of the aperture pattern would have eccentricity related errors that tend to cancel. Because the eccentricity induced oscillations in circumferential slit width are not symmetrical about the mean, the errors of the two spirals do not sum exactly to zero. Accordingly, there is a residual error "ripple" with a spatial frequency twice that of either spiral alone. In general, the ripple frequency for an N-spiral case is N times the frequency of the oscillations in circumferential slit width for any single spiral. Importantly, the amplitude of the errors in circumferential slit width decreases as the number of spirals increases.
Computer simulations show that an aperture can be designed which has minimal error given a particular eccentricity offset. In fact, if one expects a pattern with 12 bits of precision (error&lt;1/4096), assuming that the inside diameter of the spiral pattern is one inch and that the slit-edge locations can be manufactured to within .+-.0.25 microns (achievable with the methods used for integrated-circuit production), then there must be at least four but no more than nine spirals. With nine spirals an eccentricity offset of 70 microns still gives 12-bit precision. The reason for the upper bound on the number of spirals is that using more spirals forces early revolutions of the spirals (for which optimal conditions are not yet achieved) into the pattern out beyond the one-inch inner diameter, thereby degrading the achievable precision. By increasing the inside diameter of the spiral pattern, the upper bound on the number of spirals could be relaxed.
As can be appreciated, the continuous slit aperture of the present invention provides optimal performance in a confocal or other scanning microscope in that uniform masking is achieved across the entire specimen as the circumferential slit aperture is a constant percentage of the circumference taken at any point on on the specimen while a uniform resolution of image is also attained as the minimum slit width is substantially constant after more than just a very few of the first revolutions of the slit about the origin. Thus, if these inner revolutions are not used to scan the specimen, substantially uniforms, masking and uniform image resolution are achieved with the continuous slit aperture of the present invention. The result is spatially uniform image intensity and resolution, both of which are critical to the extraction of quantitative information from the images.
While the principal advantages and features of the present invention have been explained above, a greater understanding of the invention may be attained by referring to the drawing and detailed description of the preferred embodiment which follow.